Simplify the following expression: $ k = \dfrac{-8}{-10n + 5} - \dfrac{-10}{9} $
Explanation: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{9}{9}$ $ \dfrac{-8}{-10n + 5} \times \dfrac{9}{9} = \dfrac{-72}{-90n + 45} $ Multiply the second expression by $\dfrac{-10n + 5}{-10n + 5}$ $ \dfrac{-10}{9} \times \dfrac{-10n + 5}{-10n + 5} = \dfrac{100n - 50}{-90n + 45} $ Therefore $ k = \dfrac{-72}{-90n + 45} - \dfrac{100n - 50}{-90n + 45} $ Now the expressions have the same denominator we can simply subtract the numerators: $k = \dfrac{-72 - (100n - 50) }{-90n + 45} $ Distribute the negative sign: $k = \dfrac{-72 - 100n + 50}{-90n + 45}$ $k = \dfrac{-100n - 22}{-90n + 45}$ Simplify the expression by dividing the numerator and denominator by -1: $k = \dfrac{100n + 22}{90n - 45}$